Orbits of One-Dimensional Cellular Automata Induced by Symmetry Transformations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915532228263936 |
|---|---|
| author | Schaller, Martin Svozil, Karl |
| author_facet | Schaller, Martin Svozil, Karl |
| contents | Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their product is presented. Orbits are classified by their isomorphism type. Results for the number of orbits and the number of orbits by type for state sets of size two and three are included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbits of One-Dimensional Cellular Automata Induced by Symmetry Transformations Schaller, Martin Svozil, Karl Cellular Automata and Lattice Gases Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their product is presented. Orbits are classified by their isomorphism type. Results for the number of orbits and the number of orbits by type for state sets of size two and three are included. |
| title | Orbits of One-Dimensional Cellular Automata Induced by Symmetry Transformations |
| topic | Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2501.17716 |